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3 years ago

If a train is moving 72 km/h on a road of 360 km, how much time will it take to arrive?

Mathematics

2 answers:

zloy xaker [14]3 years ago

6 0

It should 5 hours. You do 360 divided by 72 and get 5

slega [8]3 years ago

3 0

"<span>I'm assuming this is just a rate problem not a more complex physics answer. Think about it this way:

72 kilometers is 72,000 meters, and an hour is 60 minutes of 60 seconds each, meaning an hour is 3600 seconds (60m*60s). This means that in 3600 seconds the car travels 72,000 meters. You can figure out how many meters are travelled per second by dividing 72,000 meters by 3,600 seconds, giving you 20 meters per second. This would give you an answer of 80 meters in 4 seconds, not 120 m. I don't know how to account for that disparity, but 80 meters would be the correct answer. If there is any other information in the problem it is probably important."</span>

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Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let $f(x)=\sqrt{x}$ and $g(x)=7x^2+4x+1$ . Then, the given equation is essentially $f(g(x))=\sqrt{7x^2+4x+1}$ . Thus, we can use the chain rule.

Recall the chain rule: $\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)$ . So, let's find the derivative of each function:

$f(x)=\sqrt{x}=x^\frac{1}{2}$

We can use the Power Rule here:

$f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}$

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Again, use the Power Rule and Sum Rule

$g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4$

Now, we can put them together:

$y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)$

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